# Tagged Questions

**0**

votes

**1**answer

75 views

### Constructing measures with support in a given set

I've recently come across the Frostmann Lemma (http://en.wikipedia.org/wiki/Frostman_lemma). Its proof involves constructing a measure with certain properties on a given subset of $\mathbb{R}^n$ (I'm ...

**9**

votes

**0**answers

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### Decay rate of measures on Cantor set

I've read that Kahane and Salem show that if $\mu$ is any measure supported on the ternary Cantor set, then $\hat{\mu}(\xi) \not\to 0$ as $|\xi| \to \infty$, however I have been unable to find a ...

**11**

votes

**4**answers

661 views

### Fourier decay rate of Cantor measures

For $0<\theta<\frac{1}{2}$, denote by $C_\theta$ the Cantor set with dissection ratio $\theta$, i.e. the Cantor set obtained from dissection parttern $(\theta, 1-2\theta,\theta)$. It is known ...

**3**

votes

**5**answers

815 views

### Reference for the iterated function system of the Koch snowflake

Let $KS$ be the Koch snowflake. This fractal has an iterated function system (IFS) of the form
$$ KS = \bigcup_{0 \leq k \leq 6} f_k(KS) $$
with
$$ f_0(z)=\frac{1}{\sqrt{3}} e^{i\pi/2} z $$
and for $0 ...